Below are listed rank-two temperaments supported by the 12edo patent val, below the indicated cutoff in TE badness.

5-limit temperaments with badness below 0.1

Listed is the wedgie and the TE complexity for six temperaments with badness less than 0.1.

Rank	Wedgie	Name	Complexity	Commas
1	<<1 4 4]]	Meantone	1.523	81/80
2	<<3 0 -7]]	Augmented	1.549	128/125
3	<<4 4 -3]]	Diminished	1.826	648/625
4	<<2 -4 -11]]	Srutal	2.121	2048/2025
5	<<1 -8 -15]]	Helmholtz	3.103	32805/32768
6	<<12 -84 -161]]	Atomic	33.065	|161 -84 -12>

7-limit temperaments with badness below 0.06

Listed is the wedgie and the TE complexity for 18 temperaments with badness less than 0.06.

Rank	Wedgie	Name	Complexity	Commas
1	<<1 4 -2 4 -6 -16]]	Dominant	1.466	36/35 64/63
2	<<4 4 4 -3 -5 -2]]	Diminished	1.494	36/35 50/49
3	<<3 0 6 -7 1 14]]	August	1.655	36/35 128/125
4	<<2 -4 -4 -11 -12 2]]	Pajara	1.953	50/49 64/63
5	<<1 4 10 4 13 12]]	Meantone	2.204	81/80 126/125
6	<<2 8 8 8 7 -4]]	Injera	2.205	50/49 81/80
7	<<3 0 -6 -7 -18 -14]]	Augene	2.336	64/63 126/125
8	<<5 8 2 1 -11 -18]]	Ripple	2.454	36/35 2560/2401
9	<<1 -8 -2 -15 -6 18]]	Schism	2.544	64/63 360/343
10	<<6 0 0 -14 -17 0]]	Hexe	2.689	50/49 128/125
11	<<0 0 12 0 19 28]]	Catler	3.026	81/80 128/125
12	<<3 -12 -30 -26 -56 -36]]	Misty	3.656	3136/3125 5120/5103
13	<<1 -8 -14 -15 -25 -10]]	Garibaldi	3.823	225/224 3125/3087
14	<<2 -4 -16 -11 -31 -26]]	Diaschismic	4.290	126/125 2048/2025
15	<<0 12 24 19 38 22]]	Compton/Waage	5.927	225/224 250047/250000
16	<<4 -8 -20 -22 -43 -24]]	Bidia	5.940	2048/2025 3136/3125
17	<<2 -16 -40 -30 -69 -48]]	Bischismic	10.110	3136/3125 32805/32768
18	<<3 -24 -54 -45 -94 -58]]	Term	13.877	32805/32768 250047/250000

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE complexity for 40 temperaments with badness less than 0.05.